Fine-Scale Statistics for the Multidimensional Farey Sequence

By Jens Marklof. 2012

34 citations recorded by the source corpus.

We generalize classical results on the gap distribution (and other fine-scale statistics) for the one-dimensional Farey sequence to arbitrary dimension. This is achieved by exploiting the equidistribution of horospheres in the space of lattices, and the equidistribution of Farey points in a certain subspace of the space of lattices. The argument follows closely the general approach developed by A. Strombergsson and the author [Ann. Math. 172:1949–2033, 2010].

Subfields: Applied Mathematics, Discrete Mathematics and Combinatorics, Geometry and Topology

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Jayadev S. Athreya
2. Berk Ustun
3. Y. Cheung
4. Cynthia Rudin
5. Artur Avila
6. S. Gouëzel

In Discrete Mathematics and Combinatorics

1. Jayadev S. Athreya
2. Berk Ustun
3. Y. Cheung
4. Cynthia Rudin

In Geometry and Topology

1. Jayadev S. Athreya
2. Berk Ustun
3. Y. Cheung
4. Cynthia Rudin
5. Artur Avila
6. S. Gouëzel

Citations in the corpus

• Supersparse linear integer models for optimized medical scoring systems (2015, methodology): “In particular, we express the generalization bound from Theorem 2 using the P -dimensional Farey points of level Λ (see Marklof, 2012, for a definition).”
• A Poincar\'e section for horocycle flow on the space of lattices (2012, background): “For similar applications in the context of higher dimensional generalizations of Farey sequences we refer the reader to [30] and [29].”